How do I convert a particle size distribution to a mass basis and calculate specific surface area?

To convert the size distribution to a mass basis and calculate the specific surface area, we will follow these steps:

1. Determine the mean diameter for each size range.
2. Calculate the volume of a single particle for each mean diameter.
3. Calculate the mass of a single particle using the given density.
4. Calculate the total mass for each size range.
5. Calculate the mass fraction for each size range.
6. Calculate the surface area of a single particle for each mean diameter.
7. Calculate the total surface area for each size range.
8. Sum the total mass and total surface area to find the specific surface area.

Given:
Density $\